Problem: Solve for $x$ and $y$ using elimination. ${6x+5y = 47}$ ${5x+6y = 52}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-5$ and the bottom equation by $6$ ${-30x-25y = -235}$ $30x+36y = 312$ Add the top and bottom equations together. $11y = 77$ $\dfrac{11y}{{11}} = \dfrac{77}{{11}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {6x+5y = 47}\thinspace$ to find $x$ ${6x + 5}{(7)}{= 47}$ $6x+35 = 47$ $6x+35{-35} = 47{-35}$ $6x = 12$ $\dfrac{6x}{{6}} = \dfrac{12}{{6}}$ ${x = 2}$ You can also plug ${y = 7}$ into $\thinspace {5x+6y = 52}\thinspace$ and get the same answer for $x$ : ${5x + 6}{(7)}{= 52}$ ${x = 2}$